The history of fractional calculus is a long one.
A question on this topic appeared earlier today. This is a nice example of a minimal version of a global fractional derivative in a Fourier sense. But many other techniques also exist. For example using Cauchy theorem for repeated integration.
How could we combine global methods such as the Fourier ones with local estimators, for example FIR filter approximants (circular or zero padded)?
Both references to previous works as well as outlines for methods are welcome.